As described in Table 1, definitional knowledge refers to knowledge gained by defining ideas or concepts such that their definitions are not uncontroversial or readily accepted by stakeholders. For definitional knowledge, Kclm = Kprv andKinf = ∅. Since such pieces of knowledge correspond to mere definitions of ideas, they are always true (tautology). From an epistemological sense, such knowledge qualifies as analytic a priori knowledge, as described in Section 2. This type of knowledge can be further explained using examples discussed in the section 4.
Deductive knowledge implies knowledge gained by establishing relationships among definitional knowledge with the aid of a logical process called deduction. Mathematically,
\(Deduction:\ \left(A\rightarrow B\right)\land\left(A\right)\vdash B,\ \ \left(\left(A\rightarrow B\right)\land\left(B\rightarrow C\right)\right)\vdash\left(A\rightarrow C\right)\)(2)
In the above equation, A , B , and C are, by definition, true entities; that is, they qualify as definitional knowledge.
Thus, from the viewpoint of deductive knowledge,KclmKprv ,Kinf = Deduction , andKprv represent pieces of definitional knowledge. From an epistemological sense, deductive knowledge refers to synthetic a priori knowledge or relations of ideas, as described in section 2. There exist two categories of deductive knowledge—(a ) primary relation of ideas and (b ) secondary relation of ideas—as exemplified in section 4.
Inductive knowledge refers to knowledge gained by experiencing the world with the aid of a logical process called induction. Mathematically,
\(Induction:\ \left(O_{1},\ldots,O_{n}\right)\vdash\left(A\rightarrow B\right)\)(3)
In the above expression,O 1,…,On refer to finite observations, experimental results, experiences, and data. Entities A and B are consistent with objects related toO 1,…,On . Thus, from the viewpoint of inductive knowledge, KclmKprv , Kinf =Induction , and Kprv correspond to pieces of data and/or observations; that is,O 1,…,On , as described above. Based on the nature of induction, inductive knowledge can be classified into three main categories—(a ) informal-induction-based knowledge; (b ) relation-of-ideas-assisted inductive knowledge; and (c ) complex-induction-based knowledge. These categories have also been exemplified in section 4.
Formulation of creative knowledge is caused by creative activities or pragmatic preferences. In this case, there exists no formal provenance; i.e., Kprv = ∅, and the logical process involved most likely corresponds to abduction; that is,Kinf = Abduction (e.g., introducing plausible causes (A 1, A 2,…) for achieving a given effect (B ).
\(Abduction:\ \left(Unknow\ A\rightarrow B\right)\land\left(B\right)\vdash Plausable\ A1,\ A2,\ldots\)(4)
It is remarkable that the truthiness of A 1, A 2,… is neither true nor false until a new piece of deductive or inductive knowledge is available. The truthiness may refer to Kantian categories of judgment, as described in section 2. Creative knowledge can be categorized into three types—(a ) analytic a-priori-based; (b ) synthetic a-priori-based; and (c ) synthetic a posteriori-based—as exemplified in section 4.
Knowledge types and their categories, except definitional knowledge, cannot exist independently. As a result, knowledge chains form. A knowledge chain manifests itself a concept map or network, or a set of concept maps or networks. In other words, when a concept map or network is studied, its contents boil down to definitional, deductive, inductive, and/or creative knowledge. Consequently, while constructing concept maps for use in desired purposes (e.g., human learning or learning in human–cyber-physical systems), their contents can be organized and analyzed in terms of knowledge types and categories presented above.
4. Exemplifications
This section presents examples that describe the types and categories of knowledge presented in Section 3. Most of the examples are relevant to arbitrary scenarios underlying engineering design and manufacturing. In all examples, a knowledge graph (concept map) represents knowledge claim (Kclm ), and in some cases, the concept maps directly point to relevant knowledge provenance (Kprv ). In other cases,Kprv is either shown partially or not shown at all. Knowledge inference (Kinf ) refers to an equation out of equations (2)–(4), as appropriate, and it is not explicitly shown in respective concept maps.
4.1. Definitional Knowledge
As already mentioned, definitional knowledge is created by uncontroversial definitions of ideas or concepts, and it does not rely on formal inference per se. At the same time, knowledge provenance cannot be separated from knowledge claim. For example, consider an illustration of turning (a widely used manufacturing process) and the corresponding concept map depicted in Figures 1(a ) and 1(b ), respectively. The concept map captures a portion of the knowledge underlying the scenario. It boils down to the following statements—(1) Force acting along the cutting direction is called cutting force; (2) Cutting speed refers to the speed at which the workpiece makes contact with the cutting tool while turning; (3) Turning is a manufacturing process that removes materials from a workpiece via chip formation; and (4) If the cutting force equals zero, no chip formation occurs. Since these statements define the concepts of cutting speed and cutting force during the material-removal process called turning, they can only be considered pieces of definitional knowledge. Thus, the above statements can be considered knowledge claim and provenance simultaneously. Without these definitions, other types or categories of knowledge underlying turning (described below) do not make sense.